Design optimization of a TetraSpar-type floater and tower for the IEA Wind 15 MW reference wind turbine

We present an optimization study for the conceptual design of wind turbine floaters of the TetraSpar type. The optimization variables include all geometric dimensions of the floater, keel, mooring lines and tower design. A gradient based optimization method is applied to a mass proportional objective cost function. The objective function accounts for the different weight components of the floater, including secondary steel, the wind turbine tower, and the mooring system. A frequency domain response method is utilized, so that each design evaluation also takes into account the dynamic response for 12 wind speeds with associated wave conditions. Nineteen constraints are applied for static and dynamic response, natural frequencies, and fatigue at the bottom of the tower. Two reference designs are presented, namely one with a soft–stiff tower and one with a stiff–stiff tower. Due to the anti-phase coupling of the floater pitch and tower vibration, the soft–stiff tower needs a stronger floater stiffness in pitch. This design thus has a larger water plane area moment than the more compact stiff–stiff floater, which is found to be the least economical. A constraint analysis is next presented based on Lagrange multipliers and a relative cost index. We find that the strongest cost influence is exerted by the 3P tower frequency constraint for the stiff-stiff and soft-stiff designs. Finally, a third design variant with a free optimizable tower frequency is introduced. This design is found to be 11% cheaper than the soft–stiff design and highlights the potential cost savings of tower designs within the 3P region.